论文标题
功率斐波那契序列的周期性模量a fibonacci编号
Periodicity of power Fibonacci sequences modulus a Fibonacci number
论文作者
论文摘要
令$ {\ Mathcal f} =（f_i：i \ ge 0）$为fibonacci数字的序列，而$ j $和$ e $是非整数。我们研究功率fibonacci序列的周期性$ {\ MATHCAL F}^e（f_j）=（f_i^e \ pmod {f_j}：i \ ge 0）$。结果表明，对于每$ j，e \ ge 1 $，序列$ {\ mathcal f}^e（f_j）$都是周期性的，并且计算其周期性。结果以前以$ {\ Mathcal f}（f_j）$而闻名；也就是说，对于$ e = 1 $。对于$ e \ in \ {1，2 \} $，获得了归一化残基的值$ρ_i\ equiv f_i^e \ pmod {f_j} $，带有$ 0 \ leρ_i<f_j-1 $。
Let ${\mathcal F}=(F_i:i\ge 0)$ be the sequence of Fibonacci numbers, and $j$ and $e$ be non negative integers. We study the periodicity of the power Fibonacci sequences ${\mathcal F}^e(F_j)=(F_i^e\pmod{F_j}: i\ge 0)$. It is shown that for every $j,e\ge 1$ the sequence ${\mathcal F}^e(F_j)$ is periodic and its periodicity is computed. The result was previously known for ${\mathcal F}(F_j)$; that is, for $e=1$. For $e\in \{1, 2\}$, the values of the normalized residues $ρ_i\equiv F_i^e\pmod{F_j}$ with $0\le ρ_i<F_j-1$ are obtained.
